Recently it has been revealed that when approaching the glass-transition temperature, T(g), the dynamics of a liquid not only drastically slows down, but also becomes progressively more heterogeneous. From our simulations and experiments of six different glass-forming liquids, we find that the heterogeneous dynamics is a result of critical-like fluctuations of static structural order, contrary to a common belief that it is purely of dynamic origin. The static correlation length and susceptibility of a structural order parameter show Ising-like power-law divergence towards the ideal glass-transition point. However, this structural ordering accompanies little density change, which explains why it has not been detected by the static structure factor so far. Our results suggest a far more direct link than thought before between glass transition and critical phenomena. Indeed, the glass transition may be a new type of critical phenomenon where a structural order parameter is directly linked to slowness.